The invention relates to the field of active filter circuits, and in particular to an active filter circuit with an operational amplifier which serves to construct higher-order low-pass filters.
Higher-order low-pass filters can be realized by cascading second-order sections or second-order sections and a first-order section without feedback. Such filter circuits avoid the use of inductors, but require an active circuit in the form of an idealized amplifier, which is generally an operational amplifier. With this idealized amplifier, active negative or positive feedback is implemented and the absence of feedback within and outside the respective low-pass filter is ensured.
Various realizations of second-order low-pass filters with operational amplifiers are known including for example, active filter circuits with three operational amplifiers (FIG. 1), active filter circuits with multiple negative feedback (FIG. 2), and active filter circuits with single positive feedback (FIG. 3). All these circuits realize the transfer function of a second-order low-pass filter with a known transfer function that can be expressed as:
                              G          ⁡                      (            p            )                          =                              v            ′                                1            +                          a              ·                              p                                  ω                  g                                                      +                          b              ·                                                p                  2                                                  ω                  g                  2                                                                                        EQ        .                                  ⁢                  (          1          )                    where    p=Laplace operator    ωg=cutoff frequency of low-pass filter    v′=passband gain of low-pass filter    a=first filter coefficient of transfer function    b=second filter coefficient of transfer function
The dimensionless filter coefficients a and b of the transfer function G(p) are set by choosing appropriate parameters for the respective RC network. With these coefficients and by connecting such low-pass filters, generally filters with different filter coefficients, in series without feedback, filters with predetermined characteristics can be realized. Known examples of different filter types are Bessel, Butterworth, and Chebyshev filters. These filter types differ by the different filter coefficients ai and bi. More detailed explanations can be found, for example, in U. Tietze and Ch. Schenk, “Halbleiter-Schaltungstechnik”, 10th Edition, Springer-Verlag, 1993, ISBN 3-540-56184-6, in Chapter 14.1, “Theoretische Grundlagen von Tiefpaβfiltern”, pages 391 to 413.
A disadvantage of these known circuits is that at a high cutoff frequency of the low-pass filter, the transfer function of the amplifier may influence the desired transfer function of the low-pass filter by its real frequency and phase characteristics. To avoid this or make the influence negligible, the transit frequency fT of the operational amplifier with negative feedback must be far outside the desired low-pass characteristic. The realization of a high cutoff frequency of the low-pass filter requires a transit frequency of the operational amplifier which is higher than the cutoff frequency of the low-pass filter by at least a factor of 20 to 100, depending on the accuracy required. The high-frequency charge reversal of the respective parasitic or load capacitances involves a high current drain of the operational amplifier. Therefore, the realization of the high transit frequency may not be possible at all.
Therefore, there is a need for an active filter circuit that provides an active low-pass filter with a defined characteristic for relatively high pass frequencies which avoids the disadvantage of the high current drain.